Word problem: Find equilibrium price from demand, supply

pezgrl78

New member
Joined
Apr 27, 2007
Messages
14
The demand equation for a certain type of printer is given by:

D=-200p + 35,000

The supply equation is predicted to be:

s= -p^2 + 400p - 20,000

Find the equilibrium price

Do I solve for p first in the demand equation, and then input the answer into the supply equation? I did that and then would get:
s = -175^2 + 400(175) -20,000

Am I doing this right?
 
I found that very confusing. So, I set both equations equal to give me?:

-p^2 + 400p - 20,000 = -200p +35,000

-p^2 +800p = 55,000

Am I even close?
 
Set the equations equal to each other:

\(\displaystyle \H\
- p^2 + 400p - 20,000 = - 200p + 35,000 \\
p^2 - 600p + 55,000 = 0 \\\)

Then we plug this into the quadratic formula:

\(\displaystyle \H\
\frac{{ - b \pm \sqrt {b^2 - 4(a)(c)} }}{{2(a)}} \\
\frac{{ - ( - 600) \pm \sqrt {( - 600)^2 - 4(1)(55,000)} }}{{2(1)}} \\
\frac{{600 \pm \sqrt {(140,000)} }}{2} \\
300 \pm \frac{{\sqrt {140,000} }}{2} \\\)

For practical purposes you want the positive answer (where the equilibrium is positive):

\(\displaystyle \H\
300 - \frac{{\sqrt {140,000} }}{2}\)
 
Top